數(shù)控加工中心刀庫(kù)設(shè)計(jì)【鏈?zhǔn)降稁?kù)】,鏈?zhǔn)降稁?kù),數(shù)控加工中心刀庫(kù)設(shè)計(jì)【鏈?zhǔn)降稁?kù)】,數(shù)控加工中心,設(shè)計(jì),鏈?zhǔn)? turning ly updated asse y wa fax: +46520223099. of complicated contact problems such as the cutting processes. frictional stress is proportional to normal stress. However, Childs 12 states that frictional stress is limited when the normal stress is larger than the shear flow stress. This is the case in the region around the tool tip, where the real-contact area approaches the models and suggests that variable friction models should be used in order to obtain more accurate results in FE simulations of E-mail addresses: john.lorentzonhv.se, (J. Lorentzon). 0890-6955/$ doi:10.1 method used for investigating wear. However, continuous devel- opment of numerical methods such as the finite element method this properly, it is necessary to simultaneously work with modelling wear and friction at the toolchip interface, as these alloys all contribute to tool wear. It is therefore important to understand the wear process in order to predict wear rates and discrepancy between simulated and measured geometry, cially in the region around the tool tip 11. Consequently, work is required to enable accurate tool wear simulations. T temperature is yet another problem 3, and temperature measurements 1 have shown that the temperature is higher than for steel. The high stress at the toolchip interface, the work hardening, and the high temperature involved in the machining of nickel geometry by moving the nodes of the tool. Reasonably good accuracy was achieved, and the method can be regarded as state- of-the-art in modelling of machining. However, this approach for simulation of tool wear in machining nickel-based superalloys has shown considerable 1. Introduction Nickel-based superalloys, used in among the most difficult materials designed to retain their high strength and machining thus involves forces than those found in the machining contact length is shorter, which giv toolchip interface 1. Work harden 30 percent 2, is another problem encount these alloys, as it may lead to sever The low thermal conductivity of nic -see front matter the feed was 0.1mm and the cutting speed was 0.75m/s. 2.1.2. Mesh The meshed workpiece can be seen in Fig. 1. The remeshing technique used was the advancing front quad. This mesh generator starts by creating elements along the boundary of the given outline boundary and mesh creation continues inward until the entire region has been meshed. The number of elements used was about 6000, with the minimum element size set at 2mm. As seen in Fig. 2a, finer mesh was used where the material separates around the tool tip. The tool was meshed with approximately 5000 elements, with minimum element size being 2mm. 2.1.3. Material properties Generally, the strain magnitude, the strain rate, and the temperature each have a strong influence on the material flow stress. Thus, it is necessary to capture these dependencies in the material model used, in order to correctly predict the chip formation. Here, neglecting a slight (about 10% between 1/s and ARTICLE IN PRESS Machine Tools W2. For Usuis model, a second set of parameters giving a different temperature dependency is also investigated; W3. Takayama and Muratas 17 wear rate model, including a functional dependence of absolute temperature; W4. Modified Usui wear rate model, by adding an exponent on the relative velocity; W5. Vibration-adjusted Usui model, where a constant term is added to the relative velocity to account for vibrations, which are not included in the chip formation model. 1.1.2. Friction F1. Coulomb friction model, which states that the friction force is proportional to the contact pressure; F2. Shear friction model, which states that the friction force is a fraction of the equivalent stress; F3. Coulomb friction model with two different friction coefficients, a reduced one around the tool tip and at a distance up on the rake face. 2. Tool wear model The tool wear model consists of a FE chip formation model and a wear model implemented as subroutines to calculate the wear rate at contact points, modifying the tool geometry accordingly. 2.1. Chip formation model The FE chip formation model was created using the commer- cial software MSC. Marc, which uses an updated Lagrange formulation. This means that the material is attached to the mesh, with periodic remeshing to avoid element distortion. The cutting process requires a coupled thermo-mechanical analysis, because mechanical work is converted into heat, causing thermal strains and influencing the material properties. Two types of thermal assumptions are commonly used for simulation of mechanical cutting, namely adiabatic heating and fully coupled thermalmechanical calculations. In this work a coupled, stag- gered, model has been used. This means that for each time J. Lorentzon, N. Jarvstrat / International Journal of increment the heat transfer analysis is made first, followed by the stress analysis. The time increment was set to 1.5ms in all analyses. Quasi-static analyses were used, which means that the Fig. 1. (a) Dimension of the chip formation model, scaled in mm. The start of the rake face is marked, as it will serve as a reference point in the wear profiles. (b) The measured cutting-edge shape, with the radius indicated; the measurement method is presented in Section 4.2. ARTICLE IN PRESS Fig. 3. Youngs modulus, E, specific heat, C p , thermal conductivity, K, and thermal expansion, a, from 21. Table 1 Tool material properties for the cemented carbides 4,5,22 Density (Kg/m 3 ) 11,900 4 Youngs modulus (GPa) 630 22 Poissons ratio 0.26 5 Yield limit (MPa) 4250 22 Thermal expansion 5.4C210 C06 5 Specific heat (J/KgK) 334 4 Thermal conductivity (W/mK) 100 22 Machine 10 4 /s at room temperature according to 18 and nearly zero between 10 2 /s and 10 5 /s at 3001C according to 19) strain rate dependency, a rate-independent piecewise linear plasticity model was used. Instead, the flow stress curve after 18 for high strain rate (10 4 /s) was used, see Fig. 2. The temperature trend of the flow stress is taken from 20. The other work-piece material properties 21 used can be seen in Fig. 3. The material properties of the uncoated cemented carbide tool were considered independent of temperature, and are listed in Table 1. 2.1.4. Friction at the toolchip interface In this work, three different friction descriptions have been used. In each case the friction coefficient was calibrated to correlate within 5% on the simulated and measured feed force. The feed force is the sum of the ploughing force and the friction force. However, in our case the cutting edge radius is small compared to the feed rate (see Fig. 1), limiting the ploughing effect, and consequently friction provides a considerable part of the feed force. The models used are: F1: The Coulomb friction model states that the friction force is proportional to the contact pressure through a friction coefficient, m, Eq. (1). The friction coefficient, m, was set to 1.0: s t C0ms n (1) Fig. 2. Flow stress curves (curve at room temp from 18 and thermal softening from 20). J. Lorentzon, N. Jarvstrat / International Journal of1074 F2: A shear friction model, which states that the friction force is a fraction of the equivalent stress, Eq. (2). The friction coefficient, m, was set to 1.1: s fr m s eqv 3 p (2) F3: The Coulomb friction model as for F1, but here with two different friction coefficients, m, over the toolchip interface. Around thetooltipandatadistanceupontherakeface,wherethecontact pressure is extremely high (above 1000MPa), the friction coefficient is set to 0.75. Elsewhere the friction coefficient is set to 1.1. A principle sketch of this is seen in Fig. 4. The model is a simplified representation of the physical behaviour observed by Zorev 23, that there is a cap on the friction stress at high normal stress. 2.1.5. Heat generation In the machining process heat is generated by friction and plastic deformation. The rate of specific volumetric flux due to plastic work is given by _ q f _ W p r (3) Tools a constant term is added to the relative velocity to account for vibrations not included in the chip formation model: dw dt A 00 s n v rel 10e C0B=T (8) 2.2.1. Wear model constants Constants for Usuis model (W1) were determined by Lor- entzon and Jarvstrat 11 by calibrating machining simulations Table 2 Wear model parameters for friction model F1 W1 W2 W3 A 1.25C210 C012 A 5.48C210 C015 D 1.02 B 8900 B 2000 E 75350 J. Lorentzon, N. Jarvstrat / International Journal of with measured wear rates: First, tool wear machining tests for the selected material were performed; then FE simulations were made under the same conditions; and finally the constants of the wear rate model were calculated by regression analysis, giving the constants B 8900 and A 1.82C210 C012 . This value of the B parameter is also used here, although the friction coefficient in the chip formation model differs because it is now calibrated with respect to feed force. For this reason, the A parameter was adjusted to give the same crater depth as in the experiments. The same methodology was used to calibrate A, D, A 0 and A 00 for the wear models W1, W2, W3, W4 and W5. The calibrated parameters to reach equilibrium faster; in our case this was obtained after about 1500 increments, see Fig. 5. The reason for this is that lowering the thermal capacity has are presented in Tables 2 and 3. The activation energy in W3 Eq. (6), E, was set to 75.35kJ/mol 25. 3. Analysis steps In a turning operation, a stationary condition with respect to temperature and forces will generally be reached almost im- mediately after the tool has penetrated the workpiece and subsequently the initial transient of the chip formation has been neglected in predictions of the tool wear progress. Instead, tool wear predictions are made on stationary chip formation condi- tions, and the first step in tool wear predictions is therefore to calculate the stationary chip condition. Finally, the wear model is activated in the chip formation analysis and the progress of tool wear is calculated. 3.1. Chip formation In order to reach stationary conditions in FE chip formation simulations using the Lagrangian method, the entire object, on which chip formation simulation is to be performed, must be present and meshed from the beginning of the simulation. Consequentially a transient analysis for reaching steady-state conditions would be computationally prohibitive 26. Fortu- W4 W5 10 C09 A 0 5.42C210 C013 A 00 1.08C210 C015 B 8900 B 8900 Table 3 Wear model parameters for W1 for the different friction models F1 (Coulomb) F2 (Shear) F3 (Adjusted) W1 A 1.25C210 C012 A 1.52C210 C012 A 1.08C210 C012 B 8900 B 8900 B 8900 Tools using more increments, however, would unnecessarily increase the computation time. The wear calculation corresponds to approximately 15s of dry machining, resulting in about 65mm flank wear land and about 5.3mm deep crater at rake face. Hence, the wear process is accelerated by about 10,000 times in the simulation model. Fig. 6. Schematic illustration of the system for tool wear calculations. 4.2. Measurements The cutting forces, the chip shape, the cutting edge radius, and the tool wear were all measured in these experiments. The cutting forces (the cutting force, Fc, the feed force, Ff, and the passive force, Fp) were measured for all samples using a three-component dynamometer (Kistler, Type 9121), a multi-channel charge amplifier (Kistler, Type 5017B), and a data acquisition system. The chip shape was investigated for one sample using optical microscopy. For this purpose, the chips produced during each trial were collected, mounted onto specimen holders, grounded and polished. After this, the shape was investigated and the thickness was measured from the obtained images. For calibration and experimental verification, wear profiles for the flank and the rake faces, as well as the cutting-edge radius, were measured for two cutting inserts. These measurements were performed at Toponova AB (www.toponova.se) using white-light interferometry, see e.g. 27 for a description. A schematic illustration of the tool in 3D with a cross-sectionwhere the worn and initial tool geometry was measured is presented in Fig. 7. 5. Results In this section, the impact of the wear and friction model on the simulated wear profile is presented together with measured wear profiles. Simulated temperature, relative velocity and contact pressure are also presented in order to emphasise and clarify the differences between the friction models. Finally, simulated cutting forces and chip thickness are compared with measurements. 5.1. Influence of wear model on wear profile In this section, the Coulomb friction model (F1) is used and simulated wear profiles are compared with measured profiles using different wear equations. 5.1.1. Crater wear The simulated crater wear profile using Usuis wear equation (W1) has a maximum crater depth in the upper region of the 4. Experiments Turning experiments were conducted for calibration of friction and wear parameters and for comparison of the simulated and measured wear profiles. 4.1. Experimental conditions The turning experiments were carried out in a CNC lathe under dry cutting conditions. One cutting speed, vc, 45m/min and one feed rate, f, 0.1mm/rev were evaluated. The turning length machined during each experiment was 12mm. The experiment was conducted with 3 replicates. The workpiece was a bar of aged and forged Inconel 718 that was predrilled at its end face to achieve pipe geometry in order to accomplish near orthogonal cutting conditions in the turning operation. The workpiece had a 35.6mm outer diameter and a 29mm inner diameter. The tool used for these turning experiments was a triangular, uncoated cemented carbide turning insert with a cutting width of 16mm. Tools (a) the rake face scaled to emphasise (length scale in mm), (b) the flank face scaled to emphasise (length scale in mm). ARTICLE IN PRESS 250 Machine 200 150 100 50 350 300 J. Lorentzon, N. Jarvstrat / International Journal of1078 The adjusted friction model with a reduced friction coefficient in the area closest to the tool tip (F3), however, predicts a maximum crater depth positioned at the proper location as given by the measurements, while also having the same general shape as the measured profiles. There are still some differences, such as a kink at the position where the friction coefficient is changed. However, the difference between simulations and measurements is of the same magnitude over the entire wear profile as the difference between the two measured wear profiles. 5.2.2. Flank wear Considering the wear at the flank face, the simulation using Coulomb friction (F1) underestimates the amount of wear near the tool tip, see Fig. 9. However, both the shear friction model (F2) and the adjusted friction model with reduced friction coefficient around the tool tip (F3) show good agreement with the measured wear profile at the flank face. Although, the shear friction model predicts too large a flank wear land compared to the measure- ment, contrary to the adjusted friction model also showing good agreement with respect to length of the flank wear land. can be seen in Fig.10 for the different friction models. For both the 0 -6 -6 -8 -10 -12 -14 -16 -80 -60 -40 -20 0 -5 -4 -3 -2 -1 0 Measurement Measurement Initial profile Coulomb friction (F1) Shear friction (F2) Adjusted friction (F3) Fig. 9. Simulated wear profiles using different friction models (measured wear profiles and initial tool profile as in Fig. 7); (a) the rake face scaled to emphasise (length scale in mm), (b) the flank face scaled to emphasise (length scale in mm). Coulomb model (F1) and the shear friction model (F2) with constant friction coefficients, a region can be observed where the velocity is zero or close to zero. Although the material in this part of the contact zone is stationary relative tothe tool, the chip is still moving. The sticking is caused by the internal material friction (plasticity) being lower than the friction between the chip and the tool. The velocity profile will thus be zero at the contact between the tool and the chip, gradually increasing about 40mm into the chip and then stabilizing; this phenomenon was presented by 5.3. Influence of friction on temperature, relative velocity and contact pressure In this section, predicted temperature, relative velocity and contact pressure using different friction models are presented for initial tool geometry, for stationary conditions with respect to tool forces and temperature (see Fig. 5), to emphasise and clarify the mechanism through which friction models influence wear rate. 5.3.1. Relative velocity The relative velocity between the tool and the work material Fig. 10. Velocity profile. Tools & Manufacture 48 (2008) 10721080 Desalvo and Shaw 28. The larger the friction coefficient, the larger this region of stationary, non-moving material and a large friction coefficient is necessary for good correlation between the simulated and measured feed force and contact length. However, by using a reduced friction coefficient around the tool tip, the velocity profile changes dramatically in the stagnant region (from 0.01 to 0.14mm in Fig. 10). 5.3.2. Temperature The impact of friction model on predicted temperature in the tool in contact with the work piece can be seen in Fig. 11. The highest temperature is observed using the Coulomb friction model (F1), while the lowest is observed when using a Coulomb model with reduced friction in the tool tip region (F3). The difference in temperature prediction between the models is less than approximately 401C, with the shear model (F2) predicting temperatures in between the two others. The higher predicted temperature with constant Coulomb friction (F1) than the model with reduced friction (F3) may seem counterintuitive, as the heat generated by contact friction is lower. However, the heat generated by plastic deformation is instead correspondingly higher, as the relative motion is accommodated by material deformation, and in addition to this the material remains in this zone for a longer time and consequently transports less of the generated heat away from this zone. For all models the temperature does not vary by more than about 1501C over the contact length and the shapes of the temperature profiles are very similar. It is, however, even more interesting that the temperature varies less than 251C over about three-quarter of the contact zone, from 0 to about 0.25mm in Fig. 11, the area where the tool wear is highest, as seen in Fig. 9. 5.3.3. Contact pressure Fig.12 shows that the contact stress is highest at the tip of the tool, and that the maximum contact stress is very high, above 2.5GPa. Furthermore, the contact stress at the rake face stabilizes at two plateaus, one high, close to the tool tip, and one low, further up on the rake face. Interestingly enough, the contact pressure is very similar for all the different friction models, even though the contact lengths differ to some extent. 5.3.4. Cutting forces and chip thickness In this section, simulated cutting forces, chip thicknesses and contact lengths are presented and compared with measurements, see Table 4. The feed force (F f ) was used to calibrate the chip formation model. The cutting force (F c ), the chip thickness and the however, is dramatically influenced by friction. It seems reason- adding the reasonable physical assumption that the friction coefficient is lower in the vicinity of the tool tip where the contact pressure is extremely high (F3). Note that the excellent experimental agreement in chip formation (cf. Table 4) is retained. Obviously, our friction model F3 with a change in friction parameter over a specified region is rather arbitrary, and should be replaced by an improved theoretically and experimentally founded model with similar characteristics, i.e. a cap on friction stress at high co